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What Influences A Matter's Specific Heat?

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why do different matter with the same mass require different amount of heat in order to raise it's temperature for 1 degree? what are some influential factors that causes it's difference?

It is all to do with the number of ways in which energy can be distributed among the atoms or molecules that comprise the substance. The more ways there are of doing this, the more energy has to be put in to raise the temperature by a certain amount.


The simplest example is to compare a monatomic gas such as argon with a diatomic gas, such as oxygen. Argon has 3 "translational" degrees of freedom , i.e. movement in space along the x, y z axes. Oxygen, being shaped like a dumbell (O=O)  has these 3 degrees of freedom but also two mutually perpendicular "end-over-end" rotations of the molecule, making 5 degrees of freedom.


The third rotation, along the molcular axis, cannot be excited at normal temperatures, for quantum mechanical reasons. This same is true for spinning of the Argon atom: this motion cannot be excited at realistic temperatures.    


Oxygen has also a vibrational degree of freedom but this too is not excited at normal temperature. So oxygen has a molar heat capacity 5/2R while for Argon it is 3/2R (R is the gas constant). More here: http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/shegas.html


For solids the molar heat capacity should be 3R, due to 3 vibrational modes. Each vibrational mode contributes double that of a rotation or a translation, as both potential energy and kinetic energy are increased when a vibration is excited. Liquids are more complicated and from what I read there is not a simple theory to predict these. 


There is a comparison of copper and water here, which is quite illuminating: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html#c4


Later footnote: I'm sorry but I left out something very important: all the above is viewing speciifc heat in terms of heat capacity per mole. To relate that to heat capacity per unit mass, one has to convert, using the atomic or molecular weight. 

Edited by exchemist
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